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Given a segment of circle symmetric about the $y$-axis, I'm wondering how to apply the integral $Q_x = \int y \, dA $ to find the first moment of area with respect to the $x$-axis. I'm having difficulties taking into account both the straight line and the circular portion of the segment.

Any help is greatly appreciated.

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It seems quite straightforward: assumming a circle of unit radius:

$$ Q_x = \int y \, dA =\int_{-a}^a \int_h^{\sqrt{1-x^2}} y \, dy \, dx$$

with $a=\sqrt{1-h^2}$. Where did you get stuck?

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